Quadratic Formula and Discriminant

Real or complex roots, discriminant sign, and vertex of the parabola for ax^2 + bx + c = 0.

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Formula and source

ax^2 + bx + c = 0 => x = (-b +/- sqrt(b^2 - 4ac)) / (2a). Discriminant D = b^2 - 4ac signs the root type: D > 0 two real, D = 0 one real double, D < 0 complex conjugate pair. Vertex at x = -b/(2a).

Classical algebra; mathematical fact. The closed form is attributed to Indian, Greek, and later Persian / European mathematicians; the modern algebraic form is universal.

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